You can take your truck home if it is within range, and if you have a safe place to park it. When I was out of Fontana the range was 90 miles. I lived 93 miles from there, and it was a no-go. I was then transfered to Otay Mesa, which was closer. I've never had to give up my truck for a home time, even if it was for 4 days. That mainly depends on your home terminal, and where you take your home time. If you have to give up the truck with a 2 day home time, it sounds like Phoenix. Phoenix is ----, about so many things. (self edited, by the way)
when I was there at least in OKC it was just the opposite the further you lived the better chance you could take it home.